Initial boundary value problems arise commonly in applications with engineering and natural systems governed by nonlinear partial differential equations (PDEs). Operator learning is an emerging field for solving these equations by using a neural network to learn a map between infinite dimensional input and output function spaces. These neural operators are trained using a combination of data (observations or simulations) and PDE-residuals (physics-loss). A major drawback of existing neural approaches is the requirement to retrain with new initial/boundary conditions, and the necessity for a large amount of simulation data for training. We develop a physics-informed transformer neural operator (named PINTO) that efficiently generalizes to unseen initial and boundary conditions, trained in a simulation-free setting using only physics loss. The main innovation lies in our new iterative kernel integral operator units, implemented using cross-attention, to transform the PDE solution's domain points into an initial/boundary condition-aware representation vector, enabling efficient learning of the solution function for new scenarios. The PINTO architecture is applied to simulate the solutions of important equations used in engineering applications: advection, Burgers, and steady and unsteady Navier-Stokes equations (three flow scenarios). For these five test cases, we show that the relative errors during testing under challenging conditions of unseen initial/boundary conditions are only one-fifth to one-third of other leading physics informed operator learning methods. Moreover, our PINTO model is able to accurately solve the advection and Burgers equations at time steps that are not included in the training collocation points. The code is available at https://github.com/quest-lab-iisc/PINTO
National Center for Supercomputing Applications, University of Illinois Urbana-Champaign（国家超级计算中心，伊利诺伊大学厄巴纳-香槟分校）；Beckman Institute for Advanced Science and Technology, University of Illinois Urbana-Champaign（贝克曼先进科学与技术研究所，伊利诺伊大学厄巴纳-香槟分校）；The Grainger College of Engineering, Department of Aerospace Engineering, University of Illinois Urbana-Champaign（格拉inger工程学院，航空航天工程系，伊利诺伊大学厄巴纳-香槟分校）；The Grainger College of Engineering, Department of Mechanical Science and Engineering, University of Illinois Urbana-Champaign（格拉inger工程学院，机械科学与工程系，伊利诺伊大学厄巴纳-香槟分校）；The Grainger College of Engineering, Department of Civil and Environmental Engineering, University of Illinois Urbana-Champaign（格拉inger工程学院，土木与环境工程系，伊利诺伊大学厄巴纳-香槟分校）；Civil and Urban Engineering Department, New York University Abu Dhabi（纽约大学阿布扎比分校土木与城市工程系）；Department of Industrial and Manufacturing Systems Engineering, Kansas State University（工业与制造系统工程系，堪萨斯州立大学）
PINN-Cast: Exploring the Role of Continuous-Depth NODE in Transformers and Physics Informed Loss as Soft Physical Constraints in Short-term Weather Forecasting
Residual-based Attention Physics-informed Neural Networks for Spatio-Temporal Ageing Assessment of Transformers Operated in Renewable Power Plants
Mondragon University（蒙dragon大学）；University of the Basque Country (UPV/EHU)（巴斯克大学）；Basque Centre for Applied Mathematics（巴斯克应用数学中心）；KTH, Royal Institute of Technology（皇家理工学院）；Ikerbasque, Basque Foundation for Science（巴斯克科学基金会）
Space Group Informed Transformer for Crystalline Materials Generation
Beijing National Laboratory for Condensed Matter Physics（北京凝聚态物理国家实验室）；School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China（中国科学院大学物理科学学院，北京100190，中国）；Key Laboratory of Material Simulation Methods and Software of Ministry of Education, College of Physics, Jilin University, Changchun 130012, China（教育部材料模拟方法与软件重点实验室，吉林大学物理学院，长春130012，中国）；State Key Laboratory of Superhard Materials, College of Physics, Jilin University, Changchun 130012, P. R. China（超硬材料国家重点实验室，吉林大学物理学院，长春130012，中华人民共和国）；Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, China（松山湖材料实验室，东莞，广东523808，中国）
Bayesian Physics Informed Neural Networks for Reliable Transformer Prognostics
Department of Electronics & Computing, Mondragon University（蒙龙大学电子与计算系）；Department of Physical Chemistry, University of the Basque Country (UPV/EHU)（巴斯克国家大学物理化学系）；Department of Mathematics, University of the Basque Country (UPV/EHU)（巴斯克国家大学数学系）；Department of Computer Science and Artificial Intelligence, University of the Basque Country (UPV/EHU)（巴斯克国家大学计算机科学与人工智能系）；Basque Centre for Applied Mathematics (BCAM)（巴斯克应用数学中心）；Ikerbasque, Basque Foundation for Science（巴斯克科学基金会）
Physics-Informed Neural Networks with Fourier Features and Attention-Driven Decoding
High Technology High School（高科技高中）；Institute for Gravitation and the Cosmos（引力与宇宙研究所）；The Pennsylvania State University（宾夕法尼亚州立大学）；Department of Physics（物理系）；Princeton University（普林斯顿大学）
Disentangling Aleatoric and Epistemic Uncertainty in Physics-Informed Neural Networks. Application to Insulation Material Degradation Prognostics
Department of Electronics and Computer Science（电子与计算机科学系）；Mondragon University（蒙得龙大学）；Research & Development（研发）；CARTIF Technology Centre（CARTIF技术中心）；Department of Physical Chemistry（物理化学系）；University of the Basque Country (EHU)（巴斯克国家大学（EHU））；Basque Centre for Applied Mathematics (BCAM)（巴斯克应用数学中心（BCAM））；Department of Computer Science and Artificial Intelligence（计算机科学与人工智能系）
Towards Generalized Hydrological Forecasting using Transformer Models for 120-Hour Streamflow Prediction
IIHR—Hydroscience and Engineering, University of Iowa（爱荷华大学 IIHR—水科学与工程研究所）；Civil and Environmental Engineering, University of Iowa（爱荷华大学土木与环境工程系）；Electrical and Computer Engineering, University of Iowa（爱荷华大学电气与计算机工程系）
Interpretable Physics-Informed Load Forecasting for U.S. Grid Resilience: SHAP-Guided Ensemble Validation in Hybrid Deep Learning Under Extreme Weather
1Dept. of Computer Science, Midwestern State University, Dallas, TX, USA 2O\&M Analytics, AES Clean Energy, The AES Corporation, Louisville, CO, USA 3Dept. of Information；Communication Engineering, Pabna University of Science
A Gravity-informed Spatiotemporal Transformer for Human Activity Intensity Prediction
National Engineering Research Center of Geographic Information System, China University of Geosciences (Wuhan)（中国地质大学（武汉）国家地理信息系统工程技术研究中心）；JD iCity, JD Technology（京东科技京东智能城市）
A Residual Guided strategy with Generative Adversarial Networks in training Physics-Informed Transformer Networks
College of Science, China Agricultural University（中国农业大学理学院）；College of Information and Electrical Engineering, China Agricultural University（中国农业大学信息与电气工程学院）；College of Water Resources and Civil Engineering, China Agricultural University（中国农业大学水利与土木工程学院）
Physics informed Transformer-VAE for biophysical parameter estimation: PROSAIL model inversion in Sentinel-2 imagery
African Institute for Mathematical Sciences (AIMS), Accra, Ghana（非洲数学科学研究所（AIMS））；African Institute for Mathematical Sciences (AIMS), Cape Town, South Africa（非洲数学科学研究所（AIMS））
Transformers with Physics-Informed Encodings and Simulation-Based Inference for Robust Detection of Eccentric Binary Black Holes in Pulsar Timing Array Data
Department of Physics, National University of Singapore（新加坡国立大学物理系）；Department of Mathematics, National University of Singapore（新加坡国立大学数学系）
Anisotropic Permeability Tensor Prediction from Porous Media Microstructure via Physics-Informed Progressive Transfer Learning with Hybrid CNN-Transformer
Faculty of Mathematics and Natural Sciences, University of Oslo（奥斯陆大学数学与自然科学学院）
Understanding Auditory Evoked Brain Signal via Physics-informed Embedding Network with Multi-Task Transformer
School of Mathematics, Southwest Jiaotong University（西南交通大学数学学院）；School of Computer, SWJTU-Leeds Joint School（西南交通大学-利兹学院计算机学院）；School of Computing and Artificial Intelligence, Southwest Jiaotong University（西南交通大学计算机与人工智能学院）；Chengdu University of Technology Oxford Brookes College（成都理工大学牛津布鲁克斯学院）
Cluster-Based Generalized Additive Models Informed by Random Fourier Features
Department of Mathematics and Mathematical Statistics, Umeå University（数学与统计学系，乌梅大学）；Department of Statistics, The Pennsylvania State University（统计系，宾夕法尼亚州立大学）
